1. Field of the Invention
The present invention relates to a semiconductor laser element using a gallium-nitride-contained semiconductor laser element as well as an optical information reproducing device using the same, and particularly relates to a semiconductor laser device providing a good FFP (Far Field Pattern).
2. Description of the Background Art
Such a prototype of a semiconductor laser element is already prepared that is made of a nitride-contained semiconductor material such as GaN, InN, AlN or mixed crystal thereof, and can emit light in a region from blue to ultraviolet light FIG. 22 is a schematic view showing a nitride semiconductor laser element (or light-emitting diode) disclosed in Japanese Patent Laying-Open No. 9-55560 of the same inventors, and shows a cross section of a waveguide stripe portion of the semiconductor laser taken along a plane perpendicular to a resonator. This semiconductor laser element (or light-emitting diode) includes a low-temperature buffer layer 192 which is a thin layer of GaN, AlN or AlGaN, and is formed on a sapphire substrate 191. The semiconductor laser element further includes an n-type GaN contact layer 193, an n-type lower clad layer 202, a non-doped or silicon-doped AlGaInN active layer 196 (or light-emitting layer), a p-type upper clad layer 197 and a p-type GaN contact layer 198, which are layered on buffer layer 192. A positive electrode 200 is formed on p-type contact layer 198. n-type GaN layer 193 has a partially exposed portion, on which a negative electrode 201 is formed, For forming this exposed portion, the n-type lower clad layer, active layer, p-type upper clad layer and a p-type GaN cap layer 199 located above the n-type GaN layer are partially removed.
In this semiconductor laser element, the n-type lower clad layer is configured by repetitively growing the n-type Al0.1Ga0.9N clad layer 194 of about 0.15-0.3 xcexcm in thickness and an n-type AlaGa1xe2x88x92aN (0xe2x89xa6axe2x89xa61) buffer layer 195 and about 200 xc3x85 in thickness, and thereby lower clad layer 202 having a thickness of about 1 xcexcm is prepared.
It is desired that the total thickness of the n-type lower clad layer is large from the viewpoint of preventing such a situation that the electric field distribution in the laser oscillation mode spreads to the n-type GaN contact layer, and thereby causes ripples in FFP. Due to difficulty in crystal growth, however, the thickness of the n-type Al0.1Ga0.9N clad layer, which can be grown on the n-type GaN layer with good yield, is restricted. Although this specification relates to the photoelectric field distribution and FFP in the semiconductor laser element structure, it particularly relates to the photoelectric field distribution and FFP in the direction perpendicular to the semiconductor multilayer film. The photoelectric field distribution and the FFP in the above direction are merely referred to as the electric field distribution and the FFP, respectively. In this semiconductor laser element, therefore, the n-type lower clad layer having a total thickness of about 1 xcexcm is formed by repetitive growth of the n-type Al0.1Ga0.9N clad layer of about 0.15-0.3 xcexcm in thickness and the n-type AlaGa1xe2x88x92aN (0xe2x89xa6axe2x89xa61) buffer layer of about 200 xc3x85.
However, the foregoing semiconductor laser element in the prior art suffers from the following problems. The inventors and others actually prepared the semiconductor laser wafer of the foregoing structure, and observed its surface with an optical microscope of a magnification of about 200 times. As a result, it was found that some wafers have fine or good surfaces, but the others have hexagonal cracks at peripheral portions. More specifically, the hexagonal cracks were found in eight among ten wafers.
Elements each formed of a portion of the wafer of the laser element structure, in which the crack was not present, were prepared. According to these element, laser oscillation occurred with a threshold current density of 2-3 kA/cm2. Elements each made of a cracked wafer portions were also prepared. According to these elements, the laser oscillation occurred only 15 among 30 elements.
As described above, the structure which employs the buffer layers containing AlN, GaN or AlGaN cannot sufficiently achieve the effect of preventing cracks, and therefore suffers from a problem of serious lowering of the yield.
An object of the invention is to overcome the foregoing problem, to provide a nitride semiconductor laser element which is optimum for application to an optical pickup or the like, and to achieve an optical information reproducing device having good light focusing characteristics.
For achieving the above object, the invention provides a nitride-contained semiconductor laser element including a layer formed of an Alx1Ga1xe2x88x92x1N (0.08xe2x89xa6x1xe2x89xa60.2) lower clad layer, an active layer formed of an alternate multilayer structure including an InwGa1xe2x88x92wN well layer and an InvGa1xe2x88x92vN barrier layer, and an Alx2Ga1xe2x88x92x2N (0.08xe2x89xa6x2xe2x89xa60.2) upper clad layer layered in this order on a substrate, one or a plurality of InzGa1xe2x88x92zN (0xe2x89xa6zxe2x89xa60.2) buffer layer(s) of 200 nm or less in thickness being disposed in the lower clad layer and/or the upper clad layer
Preferably, in the above structure, the InzGa1xe2x88x92zN (0xe2x89xa6zxe2x89xa60.2) buffer layer(s) have a thickness and a composition determined to suppress ripples in a far field pattern in a direction perpendicular to a layer surface.
Preferably, in the above structure, either or each of the upper and lower clad layers had a total thickness in a range from 0.8 xcexcm to 10 xcexcm.
Preferably, in the above structure, at least one of the InzGa1xe2x88x92zN (0xe2x89xa6zxe2x89xa60.2) buffer layers disposed in the upper and/or lower clad layers is configured such that each of the InzGa1xe2x88x92zN (0xe2x89xa6zxe2x89xa60.2) buffer layers (having a dielectric constant ∈1) and the lower/upper clad layers (having a dielectric constant ∈A, neighboring to the opposite sides form a waveguide providing a waveguide mode (effective refractive index ni, electric field distribution fi(x) in a direction perpendicular to the semiconductor layer); a waveguide layer for oscillation light of the semiconductor laser element as well as the lower clad layer and the upper clad layer form a waveguide providing a waveguide mode (effective refractive index neq, electric field distribution feq(x) in the direction perpendicular to the semiconductor layer); these waveguide modes determine a parameter F; and the buffer layer has the thickness and the composition determined to satisfy a relationship of F less than 0.4, assuming that:
F=1/{1+(xcex94/xcexa)2}
xcex94=(xcfx80/xcex)(neqxe2x88x92ni)
xcexa(xcfx89xc2x7∈0/4)∫{feq(x)*xc2x7xcex4∈(x)xc2x7fi(x)}dx
xcex4∈(x)=∈Ixe2x88x92∈A (x: within InzGa1xe2x88x92zN buffer layer), 0 (x: other than it)
xcfx89=2xcfx80c0/xcex
xcex: wavelength of oscillation light in vacuum
c0: velocity of light in vacuum
∈0: dielectric constant in vacuum
Preferably, the above structure includes a GaN lower guide layer (thickness; 0.08-0.15 xcexcm) located between the lower clad layer and the active layer, and a GaN upper guide layer (thickness: 0.08-0.15 xcexcm) located between the Alx2Ga1xe2x88x92x2N (0.08xe2x89xa6x2xe2x89xa60.2) upper clad layer and the active layer; a distance from the InzGa1xe2x88x92zN (0xe2x89xa6zxe2x89xa60.2) buffer layer disposed in the lower clad layer to the GaN upper guide layer, or a distance from the InzGa1xe2x88x92zN (0xe2x89xa6zxe2x89xa60.2) buffer layer disposed in the upper clad layer to the GaN upper guide layer is equal to d [xcexcm]; an average aluminum composition of the lower clad layer disposed in a region from the InzGa1xe2x88x92zN (0xe2x89xa6zxe2x89xa60.2) buffer layer to the GaN lower guide layer, or an average aluminum composition of the upper clad layer disposed in a region from the InGa1xe2x88x92zN (0xe2x89xa6zxe2x89xa60.2) buffer layer to the GaN upper guide layer satisfies a relationship of 0.08xe2x89xa6xxe2x89xa60.2; and a composition p1 and a thickness t1 [nm] of the buffer layer are determined to satisfy the following relationship:
0.2xe2x89xa6d less than 0.3, 10xe2x89xa6t1xe2x89xa61/(0.0080268+0.58533p1), and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.2xe2x89xa6d less than 0.3, 10xe2x89xa6t1xe2x89xa6xe2x88x928.9956+273.95p1, and 0.09 less than p1xe2x89xa60.2
or
0.2xe2x89xa6d less than 0.3, 1/(0.00017672+0.088604p1)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.2xe2x89xa6d less than 0.3, xe2x88x92103.63+2403.3p1 less than t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.3xe2x89xa6d less than 0.4, 10xe2x89xa6t1xe2x89xa61/(0.0067725+0.50578p1), and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.3xe2x89xa6d less than 0.4, 10xe2x89xa6t1xe2x89xa6xe2x88x9210.86+321.88p1, and 0.09 less than p1xe2x89xa60.2
or
0.3xe2x89xa6d less than 0.4, 1/(0.0014296+0.13014p1)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.3xe2x89xa6d less than 0.4, xe2x88x9242.254+1273.3p1xe2x89xa6t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
dxe2x89xa70.4, 10xe2x89xa6t1xe2x89xa6(0.0044063+0.3622p1)(xe2x88x921), and 0.001xe2x89xa6p1xe2x89xa60.09
or
dxe2x89xa70.4, 10xe2x89xa6t1xe2x89xa6xe2x88x9217.958+479p1, and 0.09 less than p1xe2x89xa60.2
or
dxe2x89xa70.4, (0.0031223+0.26847p1)(xe2x88x921)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
dxe2x89xa70.4, xe2x88x9225.867+664.45p1xe2x89xa6t1xe2x89xa6200, 0.09 less than p1xe2x89xa60.2
More desirably, the above structure includes a GaN lower guide layer (thickness: 0.08-0.15 xcexcm) located between the lower clad layer and the active layer, and a GaN upper guide layer (thickness: 0.08-0.15 xcexcm) located between the upper clad layer and the active layer; a distance from the InzGa1xe2x88x92zN (0xe2x89xa6zxe2x89xa60.2) buffer layer disposed in the lower clad layer to the GaN upper guide layer, or a distance from the InzGa1xe2x88x92zN (0xe2x89xa6zxe2x89xa60.2) buffer layer disposed in the upper clad layer to the GaN upper guide layer is equal to d [xcexcm]; an average aluminum composition of the lower clad layer disposed in a region from the InzGa1xe2x88x92zN (0xe2x89xa6zxe2x89xa60.2) buffer layer to the GaN lower guide layer, or an average aluminum composition of the upper clad layer disposed in a region from the InzGa1xe2x88x92zN (0xe2x89xa6zxe2x89xa60.2) buffer layer to the GaN upper guide layer satisfies a relationship of 0.08xe2x89xa6xxe2x89xa60.2; and a composition p1 and a thickness t1 [nm] of the buffer layer are determined to satisfy the following relationship:
0.2xe2x89xa6d less than 0.3, 10xe2x89xa6t1xe2x89xa6(0.0097376+0.69281p1)(xe2x88x921), and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.2xe2x89xa6d less than 0.3, 10xe2x89xa6t1xe2x89xa6xe2x88x926.6349+222.72p1, and 0.09 less than p1xe2x89xa60.2
or
0.3xe2x89xa6d less than 0.4, 10xe2x89xa6t1xe2x89xa6(0.0080268+0.58533p1)(xe2x88x921), and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.3xe2x89xa6d less than 0.4, 10xe2x89xa6t1xe2x89xa6xe2x88x928.9956+273.95p1, and 0.09 less than p1xe2x89xa60.2
or
0.3xe2x89xa6d less than 0.4, (0.0017672+0.088604p1)(1)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.3xe2x89xa6d less than 0.4, xe2x88x92103.63+2403.3p1xe2x89xa6t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.4xe2x89xa6d less than 0.8, 10xe2x89xa6t1xe2x89xa61/(0.0067725+0.50578p1), and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.4xe2x89xa6d less than 0.8, 10xe2x89xa6t1xe2x89xa6xe2x88x9210.86+321.88p1, and 0.09 less than p1xe2x89xa60.2
or
0.4xe2x89xa6d less than 0.8, 1/(0.0014296+0.13014p1)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.4xe2x89xa6d less than 0.8, xe2x88x9242.254+1273.3p1xe2x89xa6t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
dxe2x89xa70.8, 10xe2x89xa6t1xe2x89xa6(0.0044063+0.3622p1)(xe2x88x921), and 0.001xe2x89xa6p1xe2x89xa60.09
or
dxe2x89xa70.8, 10xe2x89xa6t1xe2x89xa6xe2x88x9217.958+479p1, and 0.09 less than p1xe2x89xa60.2
or
dxe2x89xa70.8, (0.0031223+0.26847p1)(xe2x88x921)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
dxe2x89xa70.8, xe2x88x9225.867+664.45p1xe2x89xa6t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
Preferably, the above structure includes a lower guide layer (thickness: 0.08-0.15 xcexcm) located between the lower clad layer and the active layer, and containing at least indium at a rate or 0% or more but smaller than 2%, and an upper guide layer (thickness: 0.08-0.15 xcexcm) located between the upper clad layer and the active layer, and containing at least indium at a rate of 0% or more but smaller than 2%; a distance from the InzGa1xe2x88x92zN (0xe2x89xa6zxe2x89xa60.2) buffer layer disposed in the lower clad layer to the GaN upper guide layer, or a distance from the InzGa1xe2x88x92zN (0xe2x89xa6zxe2x89xa60.2) buffer layer disposed in the upper clad layer to the GaN upper guide layer is equal to d [xcexcm]; an average aluminum composition of the lower clad layer disposed in a region from the InGaN buffer layer to the GaN lower guide layer, or an average aluminum composition of the upper clad layer disposed in a region from the InGaN buffer layer to the GaN upper guide layer satisfies a relationship of 0.08xe2x89xa6xxe2x89xa60.2; and a composition p1 and a thickness t1 [nm] of the buffer layer are determined to satisfy the following relationship:
dxe2x89xa70.4, 10xe2x89xa6t1xe2x89xa6(0.002182+0.2838p1)(xe2x88x921), t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
dxe2x89xa70.4, 10xe2x89xa6t1xe2x89xa6xe2x88x9227.916+631.14p1+418.94p12, t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
dxe2x89xa70.4, (xe2x88x920.0013694+0.16355p1)(xe2x88x921)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
d0.4, 60.409xe2x88x92840.5p1+10843p12xe2x89xa6t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.3xe2x89xa6d less than 0.4, 10xe2x89xa6t1xe2x89xa6(0.0028147+0.32751p1)(xe2x88x921), t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.3xe2x89xa6d less than 0.4, 10xe2x89xa6t1xe2x89xa6xe2x88x9224.449+560.59p1+222.45p12, t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.3xe2x89xa6d less than 0.4, (xe2x88x920.0011606+0.13789p1)(xe2x88x921)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.3xe2x89xa6d less than 0.4, 81.043xe2x88x921159.4p1+13537p12xe2x89xa6t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.2xe2x89xa6d less than 0.3, 10xe2x89xa6t1xe2x89xa6(0.0039942+0.39645p1)(xe2x88x921), t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.2xe2x89xa6d less than 0.3, 10xe2x89xa6t1xe2x89xa6xe2x88x9221.331+488.13p1, t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.2xe2x89xa6d less than 0.3, (xe2x88x920.00076798+0.093666p1)(xe2x88x921)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
xe2x80x830.2xe2x89xa6d less than 0.3, 108.61xe2x88x921511.6p1+19016p12xe2x89xa6t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
More desirably, the above structure includes a lower guide layer (thickness: 0.08-0.15 xcexcm) located between the lower clad layer and the active layer, and containing at least indium at a rate or 0% or more but smaller than 2%, and an upper guide layer (thickness: 0.08-0.15 xcexcm) located between the upper clad layer and the active layer, and containing at least indium at a rate of 0% or more but smaller than 2%; a distance from the InGaN buffer layer to the upper or lower guide layer is equal to d [xcexcm]; an average aluminum composition of the upper or lower clad layer disposed in a region from the InGaN buffer layer to the upper or lower guide layer satisfies a relationship of 0.08xe2x89xa6xxe2x89xa60.2; and a composition p1 and a thickness t1 [nm] of the buffer layer are determined to satisfy the following relationship:
dxe2x89xa70.4, 10xe2x89xa6t1xe2x89xa61/(0.0067725+0.50578p1), t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
dxe2x89xa70.4, 10xe2x89xa6t1xe2x89xa6xe2x88x9210.86+321.88p1, t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
dxe2x89xa70.4, 1/(0.0014296+0.13014p1)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
dxe2x89xa70.4, xe2x88x9242.254+1273.3p1xe2x89xa6t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.3xe2x89xa6d less than 0.4, 10xe2x89xa6t1xe2x89xa61/(0.0080268+0.58533p1), t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.3xe2x89xa6d less than 0.4, 10xe2x89xa6t1xe2x89xa6xe2x88x928.9956+273.95p1, and 0.09 less than p1xe2x89xa60.2
or
0.3xe2x89xa6d less than 0.4, 1/(0.00017672+0.088604p1)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.3xe2x89xa6d less than 0.4, xe2x88x92103.63+2403.3p1xe2x89xa6t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.2xe2x89xa6d less than 0.3, 10xe2x89xa6t1xe2x89xa6(0.0097376+0.69281p1)(xe2x88x921), and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.2xe2x89xa6d less than 0.3, 10xe2x89xa6t1xe2x89xa6xe2x88x926.6349+222.72p1, t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
Preferably, the above structure includes a lower guide layer (thickness: 0.08-0.15 xcexcm) located between the lower clad layer and the active layer, and containing at least indium at a rate or 2% or more but smaller than 4%, and an upper guide layer (thickness: 0.08-0.15 xcexcm) located between the upper clad layer and the active layer, and containing at least indium at a rate of 2% or more but smaller than 4%; a distance from the InzGa1xe2x88x92zN (0xe2x89xa6zxe2x89xa60.2) buffer layer disposed in the Alx1Ga1xe2x88x92x1N (0.08xe2x89xa6x1xe2x89xa60.2) lower clad layer to the GaN upper guide layer, or a distance from the InzGa1xe2x88x92zN (0xe2x89xa6zxe2x89xa60.2) buffer layer disposed in the upper clad layer to the GaN upper guide layer is equal to d [xcexcm]; an average aluminum composition of the lower clad layer disposed in a region from the InGaN buffer layer to the GaN lower guide layer, or an average aluminum composition of the upper clad layer disposed in a region from the InGaN buffer layer to the GaN upper guide layer satisfies a relationship of 0.08xe2x89xa6xxe2x89xa60.2; and a composition p1 and a thickness t1 [nm] of the buffer layer are determined to satisfy the following relationship:
dxe2x89xa70.4, 10xe2x89xa6t1xe2x89xa6(xe2x88x920.00057916+0.20257p1)(xe2x88x921), t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
dxe2x89xa70.4, 10xe2x89xa6t1xe2x89xa620.248xe2x88x92212.49p1+6390p12, t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
dxe2x89xa70.4, (xe2x88x920.0025782+0.14902p1)(xe2x88x921)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
dxe2x89xa70.4, 345.07xe2x88x926361.6p1+39339p12xe2x89xa6t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.3xe2x89xa6d less than 0.4, 10xe2x89xa6t1xe2x89xa6(xe2x88x920.000048081+0.22812p1)(xe2x88x921), t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.3xe2x89xa6d less than 0.4, 10xe2x89xa6t1xe2x89xa66.7893+7.0097p1+4779.4p12, t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.3xe2x89xa6d less than 0.4, (xe2x88x920.0024039+0.13561p1)(xe2x88x921)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.3xe2x89xa6d less than 0.4, 410.2xe2x88x927584.7p1+46101p12t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.2xe2x89xa6d less than 0.3, 10xe2x89xa6t1xe2x89xa6(xe2x88x920.000076166+0.27608p1)(xe2x88x921), t1xe2x89xa6200, and 0.001xe2x89xa6pxe2x89xa60.09
or
0.2xe2x89xa6d less than 0.3, 10xe2x89xa6t1xe2x89xa6xe2x88x924.9294+213.76p1+2827.4p12, t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.2xe2x89xa6d less than 0.3, (xe2x88x920.0018961+0.10494p1)(xe2x88x921)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.2xe2x89xa6d less than 0.3, 536.08xe2x88x929966.9p1+60707p1xe2x89xa6t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
More desirably, the above structure includes a lower guide layer (thickness: 0.08-0.15 xcexcm) located between the lower clad layer and the active layer, and containing at least indium at a rate or 2% or more but smaller than 4%, and an upper guide layer (thickness: 0.08-0.15 xcexcm) located between the upper clad layer and the active layer, and containing at least indium at a rate of 2% or more but smaller than 4%; a distance from the InzGa1xe2x88x92zN (0xe2x89xa6zxe2x89xa60.2) buffer layer disposed in the lower clad layer to the GaN upper guide layer, or a distance from the InzGa1xe2x88x92zN (0xe2x89xa6zxe2x89xa60.2) buffer layer disposed in the upper clad layer to the GaN upper guide layer is equal to d [xcexcm]; an average aluminum composition of the lower clad layer disposed in a region from the InGaN buffer layer to the GaN lower guide layer, or an average aluminum composition of the upper clad layer disposed in a region from the InGaN buffer layer to the GaN upper guide layer satisfies a relationship of 0.08xe2x89xa6xxe2x89xa60.2; and a composition p1 and a thickness t1 [nm] of the buffer layer are determined to satisfy the following relationship:
dxe2x89xa70.4, 10xe2x89xa6t1xe2x89xa6(0.002182+0.2838p1)(xe2x88x921), t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
dxe2x89xa70.4, 10xe2x89xa6t1xe2x89xa6xe2x88x9227.916+631.14p1+418.94p12, t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
dxe2x89xa70.4, (xe2x88x920 0013694+0.16355p1)(xe2x88x921)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
dxe2x89xa70.4, 60.409xe2x88x92840.5p1+10843p12xe2x89xa6t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.3xe2x89xa6d less than 0.4, 10xe2x89xa6t1xe2x89xa6(0.0028147+0.32751p1)(xe2x88x921), t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.3xe2x89xa6d less than 0.4, 10xe2x89xa6t1xe2x89xa6xe2x88x9224.449+560.59p1+222.45p12, t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.3xe2x89xa6d less than 0.4, (xe2x88x920.0011606+0.13789p1)(xe2x88x921)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.3xe2x89xa6d less than 0.4, 81.043xe2x88x921159.4p1+13537p12xe2x89xa6t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.2xe2x89xa6d less than 0.3, 10xe2x89xa6t1xe2x89xa6(0.0039942+0.39645p1)(xe2x88x921), t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.2xe2x89xa6d less than 0.3, 10xe2x89xa6t1xe2x89xa6xe2x88x9221.331+488.13p1, t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.2xe2x89xa6d less than 0.3, (xe2x88x920.00076798+0.093666p1)(xe2x88x921)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.2xe2x89xa6d less than 0.3, 108.61xe2x88x921511.6p1+19016p12xe2x89xa6t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
Preferably, the above structure includes a lower guide layer (thickness: 0.08-0.15 xcexcm) located between the lower clad layer and the active layer, and containing at least indium at a rate or 4% or more but smaller than 6%, and an upper guide layer (thickness: 0.08-0.15 xcexcm) located between the upper clad layer and the active layer, and containing at least indium at a rate of 4% or more but smaller than 6%; a distance from the InzGa1xe2x88x92zN (0xe2x89xa6zxe2x89xa60.2) buffer layer disposed in the lower clad layer to the GaN upper guide layer, or a distance from the InzGa1xe2x88x92zN (0xe2x89xa6zxe2x89xa60.2) buffer layer disposed in the upper clad layer to the GaN upper guide layer is equal to d [xcexcm]; an average aluminum composition of the lower clad layer disposed in a region from the InGaN buffer layer to the GaN lower guide layer, or an average aluminum composition of the upper clad layer disposed ill a region from the InGaN buffer layer to the GaN upper guide layer satisfies a relationship of 0.08xe2x89xa6xxe2x89xa60.2; and a composition p1 and a thickness t1 [nm] of the buffer layer are determined to satisfy the following relationship:
dxe2x89xa70.4, 10xe2x89xa6t1xe2x89xa6(xe2x88x920.0036588+0.15804p1)(xe2x88x921), t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
dxe2x89xa70.4, 10xe2x89xa6t1xe2x89xa61192.2xe2x88x9222262p1+112670p12, t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
dxe2x89xa70.4, (xe2x88x920.0035017+0.1457p1)(xe2x88x921)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
dxe2x89xa70.4, 524.75xe2x88x9210029p1+59406p12xe2x89xa6t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.3xe2x89xa6d less than 0.4, 10xe2x89xa6t1xe2x89xa6(xe2x88x920.0029727+0.18468p1)(xe2x88x921), t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.3xe2x89xa6d less than 0.4, 10xe2x89xa6t1xe2x89xa6211.87xe2x88x923874.3p1+25752p12, t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2 
or
0.3xe2x89xa6d less than 0.4, (xe2x88x920 0033291+0.13586p1)(xe2x88x921)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.3xe2x89xa6d less than 0.4, 587.7xe2x88x9211264p1+66380p12xe2x89xa6t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.2xe2x89xa6d less than 0.3, 10xe2x89xa6t1xe2x89xa6(xe2x88x920.0031947+0.21903p1)(xe2x88x921), t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.2xe2x89xa6d less than 0.3, 10xe2x89xa6t1xe2x89xa6139.37xe2x88x922496.5p1+17831p12, t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.2xe2x89xa6d less than 0.3, (xe2x88x920.0028237+0.11113p1)(xe2x88x921)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.2xe2x89xa6d less than 0.3, 766.52xe2x88x9214773p1+86589p12xe2x89xa6t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
More desirably, the above structure includes a lower guide layer (thickness; 0.08-0.15 xcexcm) located between the lower clad layer and the active layer, and containing at least indium at a rate or 4% or more but smaller than 6%, and an upper guide layer (thickness: 0.08-0.15 xcexcm) located between the upper clad layer and the active layer, and containing at least indium at a rate of 4% or more but smaller than 6%; a distance from the InzGa1xe2x88x92zN (0xe2x89xa6zxe2x89xa60.2) buffer layer disposed in the lower clad layer to the GaN upper guide layer, or a distance from the InzGa1xe2x88x92zN (0xe2x89xa6zxe2x89xa60.2) buffer layer disposed in the upper clad layer to the GaN upper guide layer is equal to d [xcexcm]; an average aluminum composition of the lower clad layer disposed in a region from the InGaN buffer layer to the GaN lower guide layer, or an average aluminum composition of the upper clad layer disposed in a region from the InGaN buffer layer to the GaN upper guide layer satisfies a relationship of 0.08xe2x89xa6xxe2x89xa60.2; and a composition p1 and a thickness t1 [nm] of the buffer layer are determined to satisfy the following relationship:
dxe2x89xa70.4, 10xe2x89xa6t1xe2x89xa6(xe2x88x920.00057916+0.20257p1)(xe2x88x921), t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
dxe2x89xa70.4, 10xe2x89xa6t1xe2x89xa620.248xe2x88x92212.49p1+6390p12, t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
dxe2x89xa70.4, (xe2x88x920.0025782+0.14902p1)(xe2x88x921)xe2x89xa6t1xe2x89xa62.00, and 0.001xe2x89xa6p1xe2x89xa60.09
or
dxe2x89xa70.4, 345.07xe2x88x926361.6p1+39339p12xe2x89xa6t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.3xe2x89xa6d less than 0.4, 10xe2x89xa6t1xe2x89xa6(xe2x88x920.000048081+0.22812p1)(xe2x88x921), t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.3xe2x89xa6d less than 0.4, 10xe2x89xa6t1xe2x89xa66.7893+7.0097p1+4779.4p12, t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.3xe2x89xa6d less than 0.4, (xe2x88x920.0024039+0.13561p1)(xe2x88x921)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.3xe2x89xa6d less than 0.4, 410.2xe2x88x927584.7p1+46101p12xe2x89xa6t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.2xe2x89xa6d less than 0.3, 10xe2x89xa6t1xe2x89xa6(xe2x88x920.000076166+0.27608p1)(xe2x88x921), t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
xe2x80x830.2xe2x89xa6d less than 0.3, 10xe2x89xa6t1xe2x89xa6xe2x88x924.9294+213.76p1+2827.4p12, t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.2xe2x89xa6d less than 0.3, (xe2x88x920.0018961+0.10494p1)(xe2x88x921)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.2xe2x89xa6d less than 0.3, 536.08xe2x88x929966.9p1+60707p1xe2x89xa6t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
Preferably, the above structure includes a lower guide layer (thickness: 0.08-0.15 xcexcm) located between the lower clad layer and the active layer, and containing at least indium at a rate or 6% or more but smaller than 7%, and an upper guide layer (thickness: 0.08-0.15 xcexcm) located between the upper clad layer and the active layer, and containing at least indium at a rate of 6% or more but smaller than 7%; a distance from the InzGa1xe2x88x92zN (0xe2x89xa6zxe2x89xa60.2) buffer layer disposed in the lower clad layer to the GaN upper guide layer, or a distance from the InzGa1xe2x88x92zN (0xe2x89xa6zxe2x89xa60.2) buffer layer disposed in the upper clad layer to the GaN upper guide layer is equal to d [xcexcm]; an average aluminum composition of the lower clad layer disposed in a region from the InGaN buffer layer to the GaN lower guide layer, or an average aluminum composition of the upper clad layer disposed in a region from the InGaN buffer layer to the GaN upper guide layer satisfies a relationship of 0.08xe2x89xa6xxe2x89xa60.2; and a composition p1 and a thickness t1 [nm] of the buffer layer are determined to satisfy the following relationship:
dxe2x89xa70.4, 10xe2x89xa6t1xe2x89xa6(xe2x88x920.0036588+0.15804p1)(xe2x88x921), t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
dxe2x89xa70.4, 10xe2x89xa6t1xe2x89xa61192.2xe2x88x9222262p1+112670p12, t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.02
or
dxe2x89xa70.4, (xe2x88x920.0041761+0.13916p1)(xe2x88x921)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
dxe2x89xa70.4, 958.16xe2x88x9218852p1+105870p12xe2x89xa6t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.3xe2x89xa6d less than 0.4, and 10xe2x89xa6t1xe2x89xa6(xe2x88x920.0038108+0.16856p1)(xe2x88x921), t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
xe2x80x830.3xe2x89xa6d less than 0.4, and 10xe2x89xa6t1xe2x89xa6973.69xe2x88x9218186p1+93321p12, t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.3xe2x89xa6d less than 0.4, and (xe2x88x920.0040339+0.13236p1)(xe2x88x921)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.3xe2x89xa6d less than 0.4, and 1056.2xe2x88x9220815p1+116460p12xe2x89xa6t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.2xe2x89xa6d less than 0.3, 10xe2x89xa6t1xe2x89xa6(xe2x88x920.0040773+0.19547p1)(xe2x88x921), t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.2xe2x89xa6d less than 0.3, 10xe2x89xa6t1xe2x89xa6539.75xe2x88x9210088p1+54757p12, t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.2xe2x89xa6d less than 0.3, (xe2x88x920.0035424+0.11285p1)(xe2x88x921)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.2xe2x89xa6d less than 0.3, 1335.8xe2x88x9226428p1+147260p12xe2x89xa6t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.02
More desirably, the above structure includes a lower guide layer (thickness: 0.08-0.15 xcexcm) located between the lower clad layer and the active layer, and containing at least indium at a rate or 6% or more but smaller than 7%, and an upper guide layer (thickness: 0.08-0.15 xcexcm) located between the upper clad layer and the active layer, and containing at least indium at a rate of 6% or more but smaller than 7%; a distance from the InzGa1xe2x88x92zN (0xe2x89xa6zxe2x89xa60.2) buffer layer disposed ill the lower clad layer to the GaN upper guide layer, or a distance from the InzGa1xe2x88x92zN (0xe2x89xa6zxe2x89xa60.2) buffer layer disposed in the upper clad layer to the CaN upper guide layer is equal to d [xcexcm]; an average aluminum composition of the lower clad layer disposed in a region from the InGaN buffer layer to the GaN lower guide layer, or an average aluminum composition of the upper-clad layer disposed in a region from the InGaN buffer layer to the GaN upper guide layer satisfies a relationship of 0.08xe2x89xa6xxe2x89xa60.2; and a composition p1 and a thickness t1 [nm] of the buffer layer are determined to satisfy the following relationship:
dxe2x89xa70.4, 10xe2x89xa6t1xe2x89xa6(xe2x88x920.0036588+0.15804p1)(xe2x88x921), t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
dxe2x89xa70.4, 10xe2x89xa6t1xe2x89xa61192.2xe2x88x9222262p1+112670p12, t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
dxe2x89xa70.4, (xe2x88x920.0035017+0.14571p1)(xe2x88x921)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
dxe2x89xa70.4, 524.75xe2x88x9210029p1+59406p12xe2x89xa6t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.3xe2x89xa6d less than 0.4, and 10xe2x89xa6t1xe2x89xa6(xe2x88x920.0029727+0.18468p1)(xe2x88x921), t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.3xe2x89xa6d less than 0.4, and 10xe2x89xa6t1xe2x89xa6211.87xe2x88x923874.3p1+25752p12, t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.3xe2x89xa6d less than 0.4, and (xe2x88x920.0033291+0.13586p1)(xe2x88x921)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.3xe2x89xa6d less than 0.4, and 587.7xe2x88x9211264p1+66380p12xe2x89xa6t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.02
or
0.2xe2x89xa6d less than 0.3, 10xe2x89xa6t1xe2x89xa6(xe2x88x920.0031947+0.21903p1)(xe2x88x921), t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.2xe2x89xa6d less than 0.3, 10xe2x89xa6t1xe2x89xa6139.37xe2x88x922496.5p1+17831p12, t1xe2x89xa6200, and 0.09xe2x89xa6p1xe2x89xa60.2
or
0.2xe2x89xa6d less than 0.3, (xe2x88x920.0028237+0.11113p1)(xe2x88x921)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.2xe2x89xa6d less than 0.3, 766.52xe2x88x9214773p1+86589p12xe2x89xa6t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
Preferably, the above structure includes a lower guide layer (thickness 0.08-0.15 xcexcm) located between the lower clad layer and the active layer, and containing at least indium at a rate or 7% or more but smaller than 10%, and an upper guide layer (thickness: 0.08-0.15 xcexcm) located between the upper clad layer and the active layer, and containing at least indium at a rate of 7% or more but smaller than 10%; a distance from the InzGa1xe2x88x92zN (0xe2x89xa6zxe2x89xa60.2) buffer layer disposed in the lower clad layer to the GaN upper guide layer, or a distance from the InzGa1xe2x88x92zN (0xe2x89xa6zxe2x89xa60.2) buffer layer disposed in the upper clad layer to the GaN upper guide layer is equal to d [xcexcm]; an average aluminum composition of the lower clad layer disposed in a region from the InGaN buffer layer to the GaN lower guide layer, or an average aluminum composition of the upper clad layer disposed in a region from the InGaN buffer layer to the GaN upper guide layer satisfies a relationship of 0.08xe2x89xa6xxe2x89xa60.2; and a composition p1 and a thickness t1 [nm] of the buffer layer are determined to satisfy the following relationship:
dxe2x89xa60.4, 10xe2x89xa6t1xe2x89xa6(xe2x88x920.004347+0.14719p1)(xe2x88x921), t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
dxe2x89xa70.4, 10xe2x89xa6t1xe2x89xa6858.55xe2x88x9216866p1+95186p12, t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
dxe2x89xa70.4, (xe2x88x920.005134+0.1362p1)(xe2x88x921)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
dxe2x89xa70.4, 2497.8xe2x88x9249961p1+264020p12xe2x89xa6t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.3xe2x89xa6d less than 0.4, and 10xe2x89xa6t1xe2x89xa6(xe2x88x920.0044872+0.15446p1)(xe2x88x921), t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.3xe2x89xa6d less than 0.4, and 10xe2x89xa6t1xe2x89xa6780.26xe2x88x9215299p1+86683p12, t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.3xe2x89xa6d less than 0.4, and (xe2x88x920.0049851+0.13106p1)(xe2x88x921)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.3xe2x89xa6d less than 0.4, and 2705.9xe2x88x9254159p1+285760p12xe2x89xa6t1 less than 200, and 0.09 less than p1xe2x89xa60.2
or
0.2xe2x89xa6d less than 0.3, 10xe2x89xa6t1xe2x89xa6(xe2x88x920.0048885+0.17591p1)(xe2x88x921), t1 less than 200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.2xe2x89xa6d less than 0.3, 10xe2x89xa6t1xe2x89xa6597.65xe2x88x9211661p1+66983p12, t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.2xe2x89xa6d less than 0.3, (xe2x88x920.0044282+0.11446p1)(xe2x88x921)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p10.09
or
0.2xe2x89xa6d less than 0.3, 3324.9xe2x88x9266656p1+351050p12xe2x89xa6t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
More desirably, the above structure includes a lower guide layer (thickness: 0.08-0.15 xcexcm) located between the lower clad layer and the active layer, and containing at least indium at a rate or 7% or more but smaller than 8, and an upper guide layer (thickness: 0.08-0.15 xcexcm) located between the upper clad layer and the active layer, and containing at least indium at a rate of 7% or more but smaller than 8; a distance from the InzGal1xe2x88x92zN (0xe2x89xa6zxe2x89xa60.2) buffer layer disposed in the lower clad layer to the GaN upper guide layer, or a distance from the InzGa1xe2x88x92zN (0xe2x89xa6z0.2) buffer layer disposed in the upper clad layer to the GaN upper guide layer is equal to d [xcexcm]; an average aluminum composition of the lower clad layer disposed in a region from the InGaN buffer layer to the GaN lower guide layer, or an average aluminum composition of the upper clad layer disposed in a region from the InGaN buffer layer to the GaN upper guide layer satisfies a relationship of 0.08xe2x89xa6xxe2x89xa60.2; and a composition p1 and a thickness t1 [nm] of the buffer layer are determined to satisfy the following relationship:
dxe2x89xa70.4, 10xe2x89xa6t1xe2x89xa6(xe2x88x920.0036588+0.15804p1)(xe2x88x921), t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
dxe2x89xa70.4, 10xe2x89xa6t1 less than 1192.2xe2x88x9222262p1+112670p12, t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
dxe2x89xa70.4, (xe2x88x920.0041761+0.13916p1)(xe2x88x921)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
dxe2x89xa70.4, 958.16xe2x88x9218852p1+105870p12xe2x89xa6t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.3xe2x89xa6d less than 0.4, and 10xe2x89xa6t1xe2x89xa6(xe2x88x920.0038108+0.16856p1)(xe2x88x921), t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.3xe2x89xa6d less than 0.4, and 10xe2x89xa6t1xe2x89xa6973.69xe2x88x9218186p1+93321p12, t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.3xe2x89xa6d less than 0.4, and (xe2x88x920.0040339+0.13236p1)(xe2x88x921)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.3xe2x89xa6d less than 0.4, and 1056.2xe2x88x9220815p1+116460p12xe2x89xa6t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.2xe2x89xa6d less than 0.3, 10xe2x89xa6t1xe2x89xa6(xe2x88x920.0040773+0.19547p1)(xe2x88x921), t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.2xe2x89xa6d less than 0.3, 10xe2x89xa6t1xe2x89xa6539.75xe2x88x9210088p1+54757p12, t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.2xe2x89xa6d less than 0.3, (xe2x88x920.0035424+0.11285p1)(xe2x88x921)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.2xe2x89xa6d less than 0.3, 1335.8xe2x88x9226428p1+147260p12xe2x89xa6t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.02
Alternatively, the above structure includes a lower guide layer (thickness: 0.08-0.15 xcexcm) located between the lower clad layer and the active layer, and containing at least indium at a rate or 8% or more but smaller than 10%, and an upper guide layer (thickness. 0.08-0.15 xcexcm) located between the upper clad layer and the active layer, and containing at least indium at a rate of 8% or more but smaller than 10%; a distance from the InzGa1xe2x88x92zN (0xe2x89xa6zxe2x89xa60.2) buffer layer disposed in the lower clad layer to the GaN upper guide layer, or a distance from the InzGa1xe2x88x92zN (0xe2x89xa6zxe2x89xa60.2) buffer layer disposed in the upper clad layer to the GaN upper guide layer is equal to d [xcexcm]; an average aluminum composition of the lower clad layer disposed in a region from the InGaN buffer layer to the GaN lower guide layer, or an average aluminum composition of the upper clad layer disposed in a region from the InGaN buffer layer to the GaN upper guide layer satisfies a relationship of 0.08xe2x89xa6xxe2x89xa60.2; and a composition p1 and a thickness t1 [nm] of the buffer layer are determined to satisfy the following relationship:
dxe2x89xa70.4, 10xe2x89xa6t1xe2x89xa6(xe2x88x920.004347+0.14719p1)(xe2x88x921), t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
dxe2x89xa70.4, 10xe2x89xa6t1xe2x89xa6858.55xe2x88x9216866p1+95186p12, t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.02
or
dxe2x89xa70.4, (xe2x88x920.005134+0.1362p1)(xe2x88x921)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
dxe2x89xa70.4, 2497.8xe2x88x9249961p1+264020p12xe2x89xa6t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.3xe2x89xa6d less than 0.4, and 10xe2x89xa6t1xe2x89xa6(xe2x88x920.0044872+0.15446p1)(xe2x88x921), t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.3xe2x89xa6d less than 0.4, and 10xe2x89xa6t1xe2x89xa6750.25xe2x88x9215299p1+86683p12, t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.3xe2x89xa6d less than 0.4, and (xe2x88x920.0049851+0.13106p1)(xe2x88x921)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.3xe2x89xa6d less than 0.4, and 2705.9xe2x88x9254159p1+285760p12xe2x89xa6t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.2xe2x89xa6d less than 0.3, 10xe2x89xa6t1xe2x89xa6(xe2x88x920.0048885+0.17591p1)(xe2x88x921), t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.2xe2x89xa6d less than 0.3, 10xe2x89xa6t1xe2x89xa6597.65xe2x88x9211661p1+66983p12, t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
or
0.2xe2x89xa6d less than 0.3, (xe2x88x920.0044282+0.11446p1)(xe2x88x921)xe2x89xa6t1xe2x89xa6200, and 0.001xe2x89xa6p1xe2x89xa60.09
or
0.2xe2x89xa6d less than 0.3, 3324.9xe2x88x9266656p1+351050p12xe2x89xa6t1xe2x89xa6200, and 0.09 less than p1xe2x89xa60.2
Preferably, at least one InzGa1xe2x88x92zN buffer layer containing indium at a rate of 0% or more but smaller than 20% is interposed between the lower clad layer and the substrate.
The invention provides an optical information reproducing device for reproducing recorded information recorded on an optical disk by performing photo-conversion of reflected light of laser light emitted onto the optical disk having an information recording surface, wherein any one of the preceding semiconductor laser elements is used as a light source
In the specification, the x-axis is perpendicular to the semiconductor layer surface. xcexa indicates a coupling coefficient between modes I and II. xcex indicates an oscillation wavelength in a vacuum. xcfx89(=2xcfx80c/xcex, c: velocity of light in vacuum) indicates an oscillation angular frequency. ∈0 indicates a dielectric constant in a vacuum. xcexc0 indicates a magnetic permeability in a vacuum. An integration range in a calculation formula of xcexa is within the n-type InGaN buffer layer, feq(x) and fi(x) satisfy the following relationship of normalization, respectively.
(neq/2/xcfx89/xcexc0)∫|feq(x)|2dx=1
(ni/2/xcfx89/xcexc0)∫|fi(x)|2dx=1
where the integration is performed in a range from a negative infinite to a positive infinite.
The foregoing and other objects, features, aspects and advantages of the present invention will become more apparent from the following detailed description of the present invention when taken in conjunction with the accompanying drawings.